Bending solutions of Levinson beams and plates in terms of the classical theories

Abstract

Using the mathematical similarity of the governing equations of the classical beam and plate theories and the Levinson beam and plate theories, and the basis of load equivalence, exact relationships between the bending solutions of the two theories for beams and plates are derived. These relationships enable the conversion of the well-known classical (Euler-Bernoulli) beam and (Kirchhoff) plate solutions to their shear deformable counterparts using the Levinson beam and plate theories. Examples are given to illustrate the use of these relationships. © 2001 Elsevier Science Ltd. All rights reserved.